tests

chore: add check for closed connector #5807

Job	Run time
unit tests (3.14)	1m 10s
integration tests (ubuntu-latest, 3.14)	1m 13s
integration tests (macos-latest, 3.14)	1m 36s
integration tests (macos-latest, 3.10)	2m 12s
integration tests (windows-latest, 3.14)	1m 55s
integration tests (windows-latest, 3.10)	1m 29s
integration tests (ubuntu-latest, 3.10)	1m 10s
unit tests (3.10)	1m 6s
	11m 51s

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